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+Require Import List.
+Require Import Arith.
+Require Import Recdef.
+Require Import Omega.
+
+Function foo (xys : (list nat * list nat)) {measure (fun xys => length (fst xys) + length (snd xys))} : list nat :=
+ match xys with
+ | (nil, _) => snd xys
+ | (_, nil) => fst xys
+ | (x :: xs', y :: ys') => match Compare_dec.nat_compare x y with
+ | Lt => x :: foo (xs', y :: ys')
+ | Eq => x :: foo (xs', ys')
+ | Gt => y :: foo (x :: xs', ys')
+ end
+ end.
+Proof.
+ intros; simpl; omega.
+ intros; simpl; omega.
+ intros; simpl; omega.
+Qed.
+
+Function bar (xys : (list nat * list nat)) {measure (fun xys => length (fst xys) + length (snd xys))} : list nat :=
+ let (xs, ys) := xys in
+ match (xs, ys) with
+ | (nil, _) => ys
+ | (_, nil) => xs
+ | (x :: xs', y :: ys') => match Compare_dec.nat_compare x y with
+ | Lt => x :: foo (xs', ys)
+ | Eq => x :: foo (xs', ys')
+ | Gt => y :: foo (xs, ys')
+ end
+ end.